Is there a biblical basis for appointing GB members? Yes, there is!
Acts 1:15-26 shows how they were selected:
(1) someone who was among Jesus early disciples, "starting with the baptism by John" (Acts 1:21-22),
(2) someone who was a witness of Jesus' resurrection (Acts 1:22),
(3) discussion with the whole congregation (Acts 1:15),
(4) group prayer (Acts 1:24), and finally,
(5) casting lots (Acts 1:26).